OFFSET
1,2
COMMENTS
Start with an infinite square grid. Each cell has eight neighbors. Place the numbers 1, 2, ..., n anywhere. Now place the numbers n+1, n+2, ..., m in order, subject to the rule that when you place k, the sum of its neighbors must equal k. Then a(n) is the maximum m that can be achieved.
This is similar to the Stepping Stones problem discussed in A337663, but predates it by more than 20 years.
As can be seen in the El Acertijo (The Riddle) links and in Rodolfo Kurchan's webpage, there are at least six similar problems, for example when the numbers are restricted to an n X n square board. All of these are worthy of inclusion in the OEIS once enough terms are known.
LINKS
El Acertijo, Number 5, Page 8, April 1993.
El Acertijo, Number 5, Page 9, April 1993.
El Acertijo, Number 5, Page 18, April 1993.
El Acertijo, Number 7, Page 15, August/September 1993.
Rudolfo Kurchan, Puzzle Fun
Giorgio Vecchi, Solution for a(5) = 36
Giorgio Vecchi, Solution for a(6) = 44
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Feb 05 2022
EXTENSIONS
a(5)-a(6) from Rodolfo Kurchan, Mar 29 2022
STATUS
approved